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arXiv · 2609.36095

A Note on the Classification of Centroaffine Hypersurfaces

Zuzanna Szancer
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Abstract

Cao and Wang recently classified a class of locally strongly convex centroaffine hypersurfaces whose non-vanishing Tchebychev vector field $T$ satisfies $K(T,X)=αX$ and $X(α)=0$ for every $X\perp T$, together with $K(T,T)=βT$. In the degenerate case $β=2α$, their higher-dimensional argument assumes in addition that the $T^\perp$-component of the difference tensor $K$ vanishes identically. We show that this extra assumption is unnecessary and the theorem can be strengthened.

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Zuzanna Szancer. 2026-09-28. A Note on the Classification of Centroaffine Hypersurfaces. https://arxiv.org/abs/2609.36095

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